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mw-ui-icon-wikimedia-expand"></span> <span>Toggle Explanation of horseshoe orbital cycle subsection</span> </button> <ul id="toc-Explanation_of_horseshoe_orbital_cycle-sublist" class="vector-toc-list"> <li id="toc-Background" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Background"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.1</span> <span>Background</span> </div> </a> <ul id="toc-Background-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Stages_of_the_orbit" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Stages_of_the_orbit"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.2</span> <span>Stages of the orbit</span> </div> </a> <ul id="toc-Stages_of_the_orbit-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Energy_viewpoint" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Energy_viewpoint"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.3</span> <span>Energy viewpoint</span> </div> </a> <ul id="toc-Energy_viewpoint-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Tadpole_orbit" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Tadpole_orbit"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Tadpole orbit</span> </div> </a> <ul id="toc-Tadpole_orbit-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-See_also" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#See_also"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>See also</span> </div> </a> <ul id="toc-See_also-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-References" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#References"> <div class="vector-toc-text"> 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mw-list-item"><a href="https://ca.wikipedia.org/wiki/%C3%92rbita_de_ferradura" title="Òrbita de ferradura – Catalan" lang="ca" hreflang="ca" data-title="Òrbita de ferradura" data-language-autonym="Català" data-language-local-name="Catalan" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Hufeisenumlaufbahn" title="Hufeisenumlaufbahn – German" lang="de" hreflang="de" data-title="Hufeisenumlaufbahn" data-language-autonym="Deutsch" data-language-local-name="German" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/%C3%93rbita_de_herradura" title="Órbita de herradura – Spanish" lang="es" hreflang="es" data-title="Órbita de herradura" data-language-autonym="Español" data-language-local-name="Spanish" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Ferra_orbita" title="Ferra orbita – Basque" lang="eu" hreflang="eu" data-title="Ferra orbita" data-language-autonym="Euskara" data-language-local-name="Basque" class="interlanguage-link-target"><span>Euskara</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D9%85%D8%AF%D8%A7%D8%B1_%D9%86%D8%B9%D9%84_%D8%A7%D8%B3%D8%A8" title="مدار نعل اسب – Persian" lang="fa" hreflang="fa" data-title="مدار نعل اسب" data-language-autonym="فارسی" data-language-local-name="Persian" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Orbite_en_fer_%C3%A0_cheval" title="Orbite en fer à cheval – French" lang="fr" hreflang="fr" data-title="Orbite en fer à cheval" data-language-autonym="Français" data-language-local-name="French" 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id="siteSub" class="noprint">From Wikipedia, the free encyclopedia</div> </div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="en" dir="ltr"><div class="shortdescription nomobile noexcerpt noprint searchaux" style="display:none">Type of co-orbital motion of a small orbiting body relative to a larger orbiting body</div> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Animation_of_(419624)_2010_SO16_orbit.gif" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/5/53/Animation_of_%28419624%29_2010_SO16_orbit.gif/350px-Animation_of_%28419624%29_2010_SO16_orbit.gif" decoding="async" width="350" height="263" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/53/Animation_of_%28419624%29_2010_SO16_orbit.gif/525px-Animation_of_%28419624%29_2010_SO16_orbit.gif 1.5x, //upload.wikimedia.org/wikipedia/commons/5/53/Animation_of_%28419624%29_2010_SO16_orbit.gif 2x" data-file-width="560" data-file-height="420" /></a><figcaption>A complex horseshoe orbit (the vertical looping is due to inclination of the smaller body's orbit to that of the Earth, and would be absent if both orbited in the same plane)<br /><style data-mw-deduplicate="TemplateStyles:r981673959">.mw-parser-output .legend{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .legend-color{display:inline-block;min-width:1.25em;height:1.25em;line-height:1.25;margin:1px 0;text-align:center;border:1px solid black;background-color:transparent;color:black}.mw-parser-output .legend-text{}</style><span class="legend nowrap"><span class="legend-color mw-no-invert" style="background-color: Yellow; color:black;"> </span>  Sun</span> <b>·</b> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r981673959"><span class="legend nowrap"><span class="legend-color mw-no-invert" style="background-color: RoyalBlue; color:white;"> </span>  Earth</span> <b>·</b> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r981673959"><span class="legend nowrap"><span class="legend-color mw-no-invert" style="background-color:Magenta; color:black;"> </span>  <a href="/wiki/(419624)_2010_SO16" title="(419624) 2010 SO16">(419624) 2010 SO16</a></span></figcaption></figure> <p>In <a href="/wiki/Celestial_mechanics" title="Celestial mechanics">celestial mechanics</a>, a <b>horseshoe orbit</b> is a type of <a href="/wiki/Co-orbital_configuration" title="Co-orbital configuration">co-orbital motion</a> of a small <a href="/wiki/Orbit" title="Orbit">orbiting</a> body relative to a larger orbiting body. The <a href="/wiki/Osculating_orbit" title="Osculating orbit">osculating</a> (instantaneous) <a href="/wiki/Orbital_period" title="Orbital period">orbital period</a> of the smaller body remains very near that of the larger body, and if its orbit is a little more eccentric than that of the larger body, during every period it appears to trace an ellipse around a point on the larger object's orbit. However, the loop is not closed but drifts forward or backward so that the point it circles will appear to move smoothly along the larger body's orbit over a long period of time. When the object approaches the larger body closely at either end of its trajectory, its apparent direction changes. Over an entire cycle the center traces the outline of a horseshoe, with the larger body between the 'horns'. </p><p>Asteroids in horseshoe orbits with respect to <a href="/wiki/Earth" title="Earth">Earth</a> include <a href="/wiki/54509_YORP" title="54509 YORP">54509 YORP</a>, <span class="nowrap"><a href="/wiki/2002_AA29" title="2002 AA29">2002 AA<span style="position: relative; top: 0.3em;"><span style="font-size:80%;">29</span></span></a></span>, <span class="nowrap"><a href="/wiki/2010_SO16" class="mw-redirect" title="2010 SO16">2010 SO<span style="position: relative; top: 0.3em;"><span style="font-size:80%;">16</span></span></a></span>, <span class="nowrap"><a href="/wiki/2015_SO2" title="2015 SO2">2015 SO<span style="position: relative; top: 0.3em;"><span style="font-size:80%;">2</span></span></a></span> and possibly <span class="nowrap"><a href="/wiki/2001_GO2" title="2001 GO2">2001 GO<span style="position: relative; top: 0.3em;"><span style="font-size:80%;">2</span></span></a></span>. A broader definition includes <a href="/wiki/3753_Cruithne" title="3753 Cruithne">3753 Cruithne</a>, which can be said to be in a compound and/or transition orbit,<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> or <span class="nowrap"><a href="/wiki/(85770)_1998_UP1" title="(85770) 1998 UP1">(85770) 1998 UP<span style="position: relative; top: 0.3em;"><span style="font-size:80%;">1</span></span></a></span> and <span class="nowrap"><a href="/wiki/2003_YN107" title="2003 YN107">2003 YN<span style="position: relative; top: 0.3em;"><span style="font-size:80%;">107</span></span></a></span>. By 2016, 12 horseshoe librators of Earth have been discovered.<sup id="cite_ref-Fuentes-horseshoe_2-0" class="reference"><a href="#cite_note-Fuentes-horseshoe-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> </p><p><a href="/wiki/Saturn" title="Saturn">Saturn</a>'s moons <a href="/wiki/Epimetheus_(moon)" title="Epimetheus (moon)">Epimetheus</a> and <a href="/wiki/Janus_(moon)" title="Janus (moon)">Janus</a> occupy horseshoe orbits with respect to each other (in their case, there is no repeated looping: each one traces a full horseshoe with respect to the other). </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Explanation_of_horseshoe_orbital_cycle">Explanation of horseshoe orbital cycle</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Horseshoe_orbit&action=edit&section=1" title="Edit section: Explanation of horseshoe orbital cycle"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Background">Background</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Horseshoe_orbit&action=edit&section=2" title="Edit section: Background"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The following explanation relates to an asteroid which is in such an orbit around the <a href="/wiki/Sun" title="Sun">Sun</a>, and is also affected by the Earth. </p><p>The asteroid is in almost the same solar orbit as Earth. Both take approximately one year to orbit the Sun. </p><p>It is also necessary to grasp two rules of orbit dynamics: </p> <ol><li>A body closer to the Sun completes an orbit more quickly than a body farther away.</li> <li>If a body accelerates along its orbit, its orbit moves outwards from the Sun. If it decelerates, the orbital radius decreases.</li></ol> <p>The horseshoe orbit arises because the gravitational attraction of the Earth changes the shape of the elliptical orbit of the asteroid. The shape changes are very small but result in significant changes relative to the Earth. </p><p>The horseshoe becomes apparent only when mapping the movement of the asteroid relative to both the Sun and the Earth. The asteroid always orbits the Sun in the same direction. However, it goes through a cycle of catching up with the Earth and falling behind, so that its movement relative to both the Sun and the Earth traces a shape like the outline of a horseshoe. </p> <div class="mw-heading mw-heading3"><h3 id="Stages_of_the_orbit">Stages of the orbit</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Horseshoe_orbit&action=edit&section=3" title="Edit section: Stages of the orbit"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Lagrange_Horseshoe_Orbit.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/d/d6/Lagrange_Horseshoe_Orbit.jpg/220px-Lagrange_Horseshoe_Orbit.jpg" decoding="async" width="220" height="222" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/d6/Lagrange_Horseshoe_Orbit.jpg/330px-Lagrange_Horseshoe_Orbit.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/d6/Lagrange_Horseshoe_Orbit.jpg/440px-Lagrange_Horseshoe_Orbit.jpg 2x" data-file-width="714" data-file-height="720" /></a><figcaption><b>Figure 1.</b> Plan showing possible orbits along gravitational contours. In this image, the Earth (and the whole image with it) is rotating counterclockwise around the Sun.</figcaption></figure> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Lagrange_Horseshoe_Thin.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/d/d5/Lagrange_Horseshoe_Thin.jpg/220px-Lagrange_Horseshoe_Thin.jpg" decoding="async" width="220" height="203" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/d5/Lagrange_Horseshoe_Thin.jpg/330px-Lagrange_Horseshoe_Thin.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/d5/Lagrange_Horseshoe_Thin.jpg/440px-Lagrange_Horseshoe_Thin.jpg 2x" data-file-width="553" data-file-height="510" /></a><figcaption><b>Figure 2.</b> Thin horseshoe orbit</figcaption></figure> <p>Starting at point A, on the inner ring between <a href="/wiki/Lagrange_point#L4_and_L5" title="Lagrange point">L<sub>5</sub></a> and Earth, the satellite is orbiting faster than the Earth and is on its way toward passing between the Earth and the Sun. But Earth's gravity exerts an outward accelerating force, pulling the satellite into a higher orbit which (per <a href="/wiki/Kepler%27s_third_law" class="mw-redirect" title="Kepler's third law">Kepler's third law</a>) decreases its angular speed. </p><p>When the satellite gets to point B, it is traveling at the same speed as Earth. Earth's gravity is still accelerating the satellite along the orbital path, and continues to pull the satellite into a higher orbit. Eventually, at Point C, the satellite reaches a high and slow enough orbit such that it starts to lag behind Earth. It then spends the next century or more appearing to drift 'backwards' around the orbit when viewed relative to the Earth. Its orbit around the Sun still takes only slightly more than one Earth year. Given enough time, the Earth and the satellite will be on opposite sides of the Sun. </p><p>Eventually the satellite comes around to point D where Earth's gravity is now reducing the satellite's orbital velocity. This causes it to fall into a lower orbit, which actually increases the angular speed of the satellite around the Sun. This continues until point E where the satellite's orbit is now lower and faster than <a href="/wiki/Earth%27s_orbit" title="Earth's orbit">Earth's orbit</a>, and it begins moving out ahead of Earth. Over the next few centuries it completes its journey back to point A. </p><p>On the longer term, asteroids can transfer between horseshoe orbits and <a href="/wiki/Quasi-satellite" title="Quasi-satellite">quasi-satellite</a> orbits. Quasi-satellites aren't gravitationally bound to their planet, but appear to circle it in a retrograde direction as they circle the Sun with the same orbital period as the planet. By 2016, orbital calculations showed that four of Earth's horseshoe librators and all five of its then known quasi-satellites repeatedly transfer between horseshoe and quasi-satellite orbits.<sup id="cite_ref-Fuentes-2016HO3_3-0" class="reference"><a href="#cite_note-Fuentes-2016HO3-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Energy_viewpoint">Energy viewpoint</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Horseshoe_orbit&action=edit&section=4" title="Edit section: Energy viewpoint"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>A somewhat different, but equivalent, view of the situation may be noted by considering <a href="/wiki/Conservation_of_energy" title="Conservation of energy">conservation of energy</a>. It is a theorem of classical mechanics that a body moving in a time-independent potential field will have its total energy, <i>E = T + V</i>, conserved, where <i>E</i> is total energy, <i>T</i> is kinetic energy (always non-negative) and <i>V</i> is potential energy, which is negative. It is apparent then, since <i>V = -GM/R</i> near a gravitating body of mass <i>M</i> and orbital radius <i>R</i>, that seen from a <i>stationary</i> frame, V will be increasing for the region behind M, and decreasing for the region in front of it. However, orbits with lower total energy have shorter periods, and so a body moving slowly on the forward side of a planet will lose energy, fall into a shorter-period orbit, and thus slowly move away, or be "repelled" from it. Bodies moving slowly on the trailing side of the planet will gain energy, rise to a higher, slower, orbit, and thereby fall behind, similarly repelled. Thus a small body can move back and forth between a leading and a trailing position, never approaching too close to the planet that dominates the region. </p> <div class="mw-heading mw-heading2"><h2 id="Tadpole_orbit">Tadpole orbit</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Horseshoe_orbit&action=edit&section=5" title="Edit section: Tadpole orbit"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Animation_of_2010_TK7.gif" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e6/Animation_of_2010_TK7.gif/220px-Animation_of_2010_TK7.gif" decoding="async" width="220" height="165" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e6/Animation_of_2010_TK7.gif/330px-Animation_of_2010_TK7.gif 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/e6/Animation_of_2010_TK7.gif/440px-Animation_of_2010_TK7.gif 2x" data-file-width="560" data-file-height="420" /></a><figcaption>An example of a tadpole orbit<br /><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r981673959"><span class="legend nowrap"><span class="legend-color mw-no-invert" style="background-color: Yellow; color:black;"> </span>  Sun</span> <b>·</b> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r981673959"><span class="legend nowrap"><span class="legend-color mw-no-invert" style="background-color: RoyalBlue; color:white;"> </span>  Earth</span> <b>·</b> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r981673959"><span class="legend nowrap"><span class="legend-color mw-no-invert" style="background-color:Magenta; color:black;"> </span>  <a href="/wiki/2010_TK7" class="mw-redirect" title="2010 TK7">2010 TK7</a></span></figcaption></figure> <dl><dd><i>See also <a href="/wiki/Trojan_(celestial_body)" title="Trojan (celestial body)">Trojan (celestial body)</a>.</i></dd></dl> <p>Figure 1 above shows shorter orbits around the <a href="/wiki/Lagrangian_point" class="mw-redirect" title="Lagrangian point">Lagrangian points</a> <a href="/wiki/Lagrange_point#L4_and_L5" title="Lagrange point">L<sub>4</sub></a> and <a href="/wiki/Lagrange_point#L4_and_L5" title="Lagrange point">L<sub>5</sub></a> (e.g. the lines close to the blue triangles). These are called <b>tadpole orbits</b> and can be explained in a similar way, except that the asteroid's distance from the Earth does not oscillate as far as the <a href="/wiki/Lagrange_point#L3" title="Lagrange point">L<sub>3</sub></a> point on the other side of the Sun. As it moves closer to or farther from the Earth, the changing pull of Earth's gravitational field causes it to accelerate or decelerate, causing a change in its orbit known as <a href="/wiki/Libration" title="Libration">libration</a>. </p><p>An example of a tadpole orbit is <a href="/wiki/Polydeuces_(moon)" title="Polydeuces (moon)">Polydeuces</a>, a small moon of <a href="/wiki/Saturn" title="Saturn">Saturn</a> which librates around the trailing <a href="/wiki/Lagrange_point#L4_and_L5" title="Lagrange point">L<sub>5</sub></a> point relative to a larger moon, <a href="/wiki/Dione_(moon)" title="Dione (moon)">Dione</a>. In relation to the orbit of Earth, the 300-metre-diameter (980-foot) asteroid <span class="nowrap"><a href="/wiki/2010_TK7" class="mw-redirect" title="2010 TK7">2010 TK<span style="position: relative; top: 0.3em;"><span style="font-size:80%;">7</span></span></a></span> is in a tadpole orbit around the leading <a href="/wiki/Lagrange_point#L4_and_L5" title="Lagrange point">L<sub>4</sub></a> point. <a href="/wiki/2020_VT1" title="2020 VT1">2020 VT1</a> follows a temporary horseshoe orbit with respect to <a href="/wiki/Mars" title="Mars">Mars</a>.<sup id="cite_ref-MarsHorseshoe_4-0" class="reference"><a href="#cite_note-MarsHorseshoe-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> </p> <div style="clear:right;" class=""></div> <table class="wikitable sortable" style="text-align: center;"> <caption>Known and suspected companions of Earth <style data-mw-deduplicate="TemplateStyles:r1129693374">.mw-parser-output .hlist dl,.mw-parser-output .hlist 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dd:first-child::before,.mw-parser-output .hlist dd dt:first-child::before,.mw-parser-output .hlist dd li:first-child::before,.mw-parser-output .hlist dt dd:first-child::before,.mw-parser-output .hlist dt dt:first-child::before,.mw-parser-output .hlist dt li:first-child::before,.mw-parser-output .hlist li dd:first-child::before,.mw-parser-output .hlist li dt:first-child::before,.mw-parser-output .hlist li li:first-child::before{content:" (";font-weight:normal}.mw-parser-output .hlist dd dd:last-child::after,.mw-parser-output .hlist dd dt:last-child::after,.mw-parser-output .hlist dd li:last-child::after,.mw-parser-output .hlist dt dd:last-child::after,.mw-parser-output .hlist dt dt:last-child::after,.mw-parser-output .hlist dt li:last-child::after,.mw-parser-output .hlist li dd:last-child::after,.mw-parser-output .hlist li dt:last-child::after,.mw-parser-output .hlist li li:last-child::after{content:")";font-weight:normal}.mw-parser-output .hlist ol{counter-reset:listitem}.mw-parser-output .hlist ol>li{counter-increment:listitem}.mw-parser-output .hlist ol>li::before{content:" "counter(listitem)"\a0 "}.mw-parser-output .hlist dd ol>li:first-child::before,.mw-parser-output .hlist dt ol>li:first-child::before,.mw-parser-output .hlist li ol>li:first-child::before{content:" ("counter(listitem)"\a0 "}</style><style data-mw-deduplicate="TemplateStyles:r1239400231">.mw-parser-output .navbar{display:inline;font-size:88%;font-weight:normal}.mw-parser-output .navbar-collapse{float:left;text-align:left}.mw-parser-output .navbar-boxtext{word-spacing:0}.mw-parser-output .navbar ul{display:inline-block;white-space:nowrap;line-height:inherit}.mw-parser-output .navbar-brackets::before{margin-right:-0.125em;content:"[ "}.mw-parser-output .navbar-brackets::after{margin-left:-0.125em;content:" ]"}.mw-parser-output .navbar li{word-spacing:-0.125em}.mw-parser-output .navbar a>span,.mw-parser-output .navbar a>abbr{text-decoration:inherit}.mw-parser-output .navbar-mini abbr{font-variant:small-caps;border-bottom:none;text-decoration:none;cursor:inherit}.mw-parser-output .navbar-ct-full{font-size:114%;margin:0 7em}.mw-parser-output .navbar-ct-mini{font-size:114%;margin:0 4em}html.skin-theme-clientpref-night .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}@media(prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}}@media print{.mw-parser-output .navbar{display:none!important}}</style><div class="navbar plainlinks hlist navbar-mini" style="float:bottom"><ul class="navbar-brackets"><li class="nv-view"><a href="/wiki/Template:Known_and_suspected_companions_of_Earth" title="Template:Known and suspected companions of Earth"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Known_and_suspected_companions_of_Earth" title="Template talk:Known and suspected companions of Earth"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Known_and_suspected_companions_of_Earth" title="Special:EditPage/Template:Known and suspected companions of Earth"><abbr title="Edit this template">e</abbr></a></li></ul></div> </caption> <tbody><tr> <th><a href="/wiki/Provisional_designation_in_astronomy#Minor_planets" title="Provisional designation in astronomy">Name</a> </th> <th><a href="/wiki/Eccentricity_(orbit)" class="mw-redirect" title="Eccentricity (orbit)">Eccentricity</a> </th> <th>Diameter<br />(<a href="/wiki/Meter" class="mw-redirect" title="Meter">m</a>) </th> <th>Discoverer </th> <th>Date of Discovery </th> <th>Type </th> <th>Current Type </th></tr> <tr> <td style="text-align:left"><a href="/wiki/Moon" title="Moon">Moon</a></td> <td>0.055</td> <td>3474800</td> <td>?</td> <td>Prehistory</td> <td><a href="/wiki/Natural_satellite" title="Natural satellite">Natural satellite</a></td> <td><a href="/wiki/Natural_satellite" title="Natural satellite">Natural satellite</a> </td></tr> <tr> <td style="text-align:left"><a href="/wiki/1913_Great_Meteor_Procession" title="1913 Great Meteor Procession">1913 Great Meteor Procession</a></td> <td>?</td> <td>?</td> <td>?</td> <td>1913-02-09</td> <td>Possible <a href="/wiki/Temporary_satellite" title="Temporary satellite">Temporary satellite</a></td> <td>Destroyed </td></tr> <tr style="background:#E9E9E9"> <td style="text-align:left"><a href="/wiki/3753_Cruithne" title="3753 Cruithne">3753 Cruithne</a></td> <td>0.515</td> <td>5000</td> <td><a href="/wiki/Duncan_Waldron" title="Duncan Waldron">Duncan Waldron</a></td> <td>1986-10-10</td> <td><a href="/wiki/Quasi-satellite" title="Quasi-satellite">Quasi-satellite</a></td> <td><a class="mw-selflink selflink">Horseshoe orbit</a> </td></tr> <tr> <td style="text-align:left"><a href="/wiki/1991_VG" title="1991 VG">1991 VG</a></td> <td>0.053</td> <td>5–12</td> <td><a href="/wiki/Spacewatch" title="Spacewatch">Spacewatch</a></td> <td>1991-11-06</td> <td><a href="/wiki/Temporary_satellite" title="Temporary satellite">Temporary satellite</a></td> <td><a href="/wiki/Apollo_asteroid" title="Apollo asteroid">Apollo asteroid</a> </td></tr> <tr style="background:#cccccc"> <td style="text-align:left"><span class="nowrap"><a href="/wiki/(85770)_1998_UP1" title="(85770) 1998 UP1">(85770) 1998 UP<span style="position: relative; top: 0.3em;"><span style="font-size:80%;">1</span></span></a></span></td> <td>0.345</td> <td>210–470</td> <td><a href="/wiki/Lincoln_Laboratory%27s_Experimental_Test_Site" class="mw-redirect" title="Lincoln Laboratory's Experimental Test Site">Lincoln Lab's ETS</a></td> <td>1998-10-18</td> <td><a class="mw-selflink selflink">Horseshoe orbit</a></td> <td><a class="mw-selflink selflink">Horseshoe orbit</a> </td></tr> <tr style="background:#cccccc"> <td style="text-align:left"><a href="/wiki/54509_YORP" title="54509 YORP">54509 YORP</a></td> <td>0.230</td> <td>124</td> <td><a href="/wiki/Lincoln_Laboratory%27s_Experimental_Test_Site" class="mw-redirect" title="Lincoln Laboratory's Experimental Test Site">Lincoln Lab's ETS</a></td> <td>2000-08-03</td> <td><a class="mw-selflink selflink">Horseshoe orbit</a></td> <td><a class="mw-selflink selflink">Horseshoe orbit</a> </td></tr> <tr style="background:#cccccc"> <td style="text-align:left"><span class="nowrap"><a href="/wiki/2001_GO2" title="2001 GO2">2001 GO<span style="position: relative; top: 0.3em;"><span style="font-size:80%;">2</span></span></a></span></td> <td>0.168</td> <td>35–85</td> <td><a href="/wiki/Lincoln_Laboratory%27s_Experimental_Test_Site" class="mw-redirect" title="Lincoln Laboratory's Experimental Test Site">Lincoln Lab's ETS</a></td> <td>2001-04-13</td> <td>Possible <a class="mw-selflink selflink">Horseshoe orbit</a></td> <td>Possible <a class="mw-selflink selflink">Horseshoe orbit</a> </td></tr> <tr style="background:#E9E9E9"> <td style="text-align:left"><span class="nowrap"><a href="/wiki/2002_AA29" title="2002 AA29">2002 AA<span style="position: relative; top: 0.3em;"><span style="font-size:80%;">29</span></span></a></span></td> <td>0.013</td> <td>20–100</td> <td><a href="/wiki/Lincoln_Near-Earth_Asteroid_Research" title="Lincoln Near-Earth Asteroid Research">LINEAR</a></td> <td>2002-01-09</td> <td><a href="/wiki/Quasi-satellite" title="Quasi-satellite">Quasi-satellite</a></td> <td><a class="mw-selflink selflink">Horseshoe orbit</a> </td></tr> <tr style="background:#E9E9E9"> <td style="text-align:left"><span class="nowrap"><a href="/wiki/2003_YN107" title="2003 YN107">2003 YN<span style="position: relative; top: 0.3em;"><span style="font-size:80%;">107</span></span></a></span></td> <td>0.014</td> <td>10–30</td> <td><a href="/wiki/Lincoln_Near-Earth_Asteroid_Research" title="Lincoln Near-Earth Asteroid Research">LINEAR</a></td> <td>2003-12-20</td> <td><a href="/wiki/Quasi-satellite" title="Quasi-satellite">Quasi-satellite</a></td> <td><a class="mw-selflink selflink">Horseshoe orbit</a> </td></tr> <tr style="background:#E9E9E9"> <td style="text-align:left"><span class="nowrap"><a href="/wiki/(164207)_2004_GU9" title="(164207) 2004 GU9">(164207) 2004 GU<span style="position: relative; top: 0.3em;"><span style="font-size:80%;">9</span></span></a></span></td> <td>0.136</td> <td>160–360</td> <td><a href="/wiki/Lincoln_Near-Earth_Asteroid_Research" title="Lincoln Near-Earth Asteroid Research">LINEAR</a></td> <td>2004-04-13</td> <td><a href="/wiki/Quasi-satellite" title="Quasi-satellite">Quasi-satellite</a></td> <td><a href="/wiki/Quasi-satellite" title="Quasi-satellite">Quasi-satellite</a> </td></tr> <tr style="background:#E9E9E9"> <td style="text-align:left"><span class="nowrap"><a href="/wiki/(277810)_2006_FV35" title="(277810) 2006 FV35">(277810) 2006 FV<span style="position: relative; top: 0.3em;"><span style="font-size:80%;">35</span></span></a></span></td> <td>0.377</td> <td>140–320</td> <td><a href="/wiki/Spacewatch" title="Spacewatch">Spacewatch</a></td> <td>2006-03-29</td> <td><a href="/wiki/Quasi-satellite" title="Quasi-satellite">Quasi-satellite</a></td> <td><a href="/wiki/Quasi-satellite" title="Quasi-satellite">Quasi-satellite</a> </td></tr> <tr style="background:#cccccc"> <td style="text-align:left"><span class="nowrap"><a href="/wiki/2006_JY26" title="2006 JY26">2006 JY<span style="position: relative; top: 0.3em;"><span style="font-size:80%;">26</span></span></a></span></td> <td>0.083</td> <td>6–13</td> <td><a href="/wiki/Catalina_Sky_Survey" title="Catalina Sky Survey">Catalina Sky Survey</a></td> <td>2006-05-06</td> <td><a class="mw-selflink selflink">Horseshoe orbit</a></td> <td><a class="mw-selflink selflink">Horseshoe orbit</a> </td></tr> <tr> <td style="text-align:left"><span class="nowrap"><a href="/wiki/2006_RH120" title="2006 RH120">2006 RH<span style="position: relative; top: 0.3em;"><span style="font-size:80%;">120</span></span></a></span></td> <td>0.024</td> <td>2–3</td> <td><a href="/wiki/Catalina_Sky_Survey" title="Catalina Sky Survey">Catalina Sky Survey</a></td> <td>2006-09-13</td> <td><a href="/wiki/Temporary_satellite" title="Temporary satellite">Temporary satellite</a></td> <td><a href="/wiki/Apollo_asteroid" title="Apollo asteroid">Apollo asteroid</a> </td></tr> <tr style="background:#cccccc"> <td style="text-align:left"><span class="nowrap"><a href="/wiki/(419624)_2010_SO16" title="(419624) 2010 SO16">(419624) 2010 SO<span style="position: relative; top: 0.3em;"><span style="font-size:80%;">16</span></span></a></span></td> <td>0.075</td> <td>357</td> <td><a href="/wiki/Wide-field_Infrared_Survey_Explorer" title="Wide-field Infrared Survey Explorer">WISE</a></td> <td>2010-09-17</td> <td><a class="mw-selflink selflink">Horseshoe orbit</a></td> <td><a class="mw-selflink selflink">Horseshoe orbit</a> </td></tr> <tr style="background:#C2FFFF"> <td style="text-align:left"><span class="nowrap"><a href="/wiki/(706765)_2010_TK7" title="(706765) 2010 TK7">(706765) 2010 TK<span style="position: relative; top: 0.3em;"><span style="font-size:80%;">7</span></span></a></span></td> <td>0.191</td> <td>150–500</td> <td><a href="/wiki/Wide-field_Infrared_Survey_Explorer" title="Wide-field Infrared Survey Explorer">WISE</a></td> <td>2010-10-01</td> <td><a href="/wiki/Earth_trojan" title="Earth trojan">Earth trojan</a></td> <td><a href="/wiki/Earth_trojan" title="Earth trojan">Earth trojan</a> </td></tr> <tr style="background:#cccccc"> <td style="text-align:left"><span class="nowrap"><a href="/wiki/2013_BS45" title="2013 BS45">2013 BS<span style="position: relative; top: 0.3em;"><span style="font-size:80%;">45</span></span></a></span></td> <td>0.083</td> <td>20–40</td> <td><a href="/wiki/Spacewatch" title="Spacewatch">Spacewatch</a></td> <td>2010-01-20</td> <td><a class="mw-selflink selflink">Horseshoe orbit</a></td> <td><a class="mw-selflink selflink">Horseshoe orbit</a> </td></tr> <tr style="background:#E9E9E9"> <td style="text-align:left"><span class="nowrap"><a href="/wiki/2013_LX28" title="2013 LX28">2013 LX<span style="position: relative; top: 0.3em;"><span style="font-size:80%;">28</span></span></a></span></td> <td>0.452</td> <td>130–300</td> <td><a href="/wiki/Pan-STARRS" title="Pan-STARRS">Pan-STARRS</a></td> <td>2013-06-12</td> <td><a href="/wiki/Quasi-satellite" title="Quasi-satellite">Quasi-satellite</a> temporary</td> <td><a href="/wiki/Quasi-satellite" title="Quasi-satellite">Quasi-satellite</a> temporary </td></tr> <tr style="background:#E9E9E9"> <td style="text-align:left"><span class="nowrap"><a href="/wiki/2014_OL339" title="2014 OL339">2014 OL<span style="position: relative; top: 0.3em;"><span style="font-size:80%;">339</span></span></a></span></td> <td>0.461</td> <td>70–160</td> <td><a href="/wiki/EURONEAR" title="EURONEAR">EURONEAR</a></td> <td>2014-07-29</td> <td><a href="/wiki/Quasi-satellite" title="Quasi-satellite">Quasi-satellite</a> temporary</td> <td><a href="/wiki/Quasi-satellite" title="Quasi-satellite">Quasi-satellite</a> temporary </td></tr> <tr style="background:#E9E9E9"> <td style="text-align:left"><span class="nowrap"><a href="/wiki/2015_SO2" title="2015 SO2">2015 SO<span style="position: relative; top: 0.3em;"><span style="font-size:80%;">2</span></span></a></span></td> <td>0.108</td> <td>50–110</td> <td><a href="/wiki/%C4%8Crni_Vrh_Observatory" title="Črni Vrh Observatory">Črni Vrh Observatory</a></td> <td>2015-09-21</td> <td><a href="/wiki/Quasi-satellite" title="Quasi-satellite">Quasi-satellite</a></td> <td><a class="mw-selflink selflink">Horseshoe orbit</a> temporary </td></tr> <tr style="background:#cccccc"> <td style="text-align:left"><span class="nowrap"><a href="/wiki/2015_XX169" title="2015 XX169">2015 XX<span style="position: relative; top: 0.3em;"><span style="font-size:80%;">169</span></span></a></span></td> <td>0.184</td> <td>9–22</td> <td><a href="/wiki/Mount_Lemmon_Survey" title="Mount Lemmon Survey">Mount Lemmon Survey</a></td> <td>2015-12-09</td> <td><a class="mw-selflink selflink">Horseshoe orbit</a> temporary</td> <td><a class="mw-selflink selflink">Horseshoe orbit</a> temporary </td></tr> <tr style="background:#cccccc"> <td style="text-align:left"><a href="/wiki/2015_YA" title="2015 YA">2015 YA</a></td> <td>0.279</td> <td>9–22</td> <td><a href="/wiki/Catalina_Sky_Survey" title="Catalina Sky Survey">Catalina Sky Survey</a></td> <td>2015-12-16</td> <td><a class="mw-selflink selflink">Horseshoe orbit</a> temporary</td> <td><a class="mw-selflink selflink">Horseshoe orbit</a> temporary </td></tr> <tr style="background:#cccccc"> <td style="text-align:left"><span class="nowrap"><a href="/wiki/2015_YQ1" title="2015 YQ1">2015 YQ<span style="position: relative; top: 0.3em;"><span style="font-size:80%;">1</span></span></a></span></td> <td>0.404</td> <td>7–16</td> <td><a href="/wiki/Mount_Lemmon_Survey" title="Mount Lemmon Survey">Mount Lemmon Survey</a></td> <td>2015-12-19</td> <td><a class="mw-selflink selflink">Horseshoe orbit</a> temporary</td> <td><a class="mw-selflink selflink">Horseshoe orbit</a> temporary </td></tr> <tr style="background:#E9E9E9"> <td style="text-align:left"><a href="/wiki/469219_Kamo%CA%BBoalewa" title="469219 Kamoʻoalewa">469219 Kamoʻoalewa</a></td> <td>0.104</td> <td>40-100</td> <td><a href="/wiki/Pan-STARRS" title="Pan-STARRS">Pan-STARRS</a></td> <td>2016-04-27</td> <td><a href="/wiki/Quasi-satellite" title="Quasi-satellite">Quasi-satellite</a> stable</td> <td><a href="/wiki/Quasi-satellite" title="Quasi-satellite">Quasi-satellite</a> stable </td></tr> <tr> <td style="text-align:left"><a href="/wiki/DN16082203" class="mw-redirect" title="DN16082203">DN16082203</a></td> <td>?</td> <td>?</td> <td>?</td> <td>2016-08-22</td> <td>Possible <a href="/wiki/Temporary_satellite" title="Temporary satellite">Temporary satellite</a></td> <td>Destroyed </td></tr> <tr> <td style="text-align:left"><span class="nowrap"><a href="/wiki/2020_CD3" title="2020 CD3">2020 CD<span style="position: relative; top: 0.3em;"><span style="font-size:80%;">3</span></span></a></span></td> <td>0.017</td> <td>1–6</td> <td><a href="/wiki/Mount_Lemmon_Survey" title="Mount Lemmon Survey">Mount Lemmon Survey</a></td> <td>2020-02-15</td> <td><a href="/wiki/Temporary_satellite" title="Temporary satellite">Temporary satellite</a></td> <td><a href="/wiki/Apollo_asteroid" title="Apollo asteroid">Apollo asteroid</a> </td></tr> <tr style="background:#cccccc"> <td style="text-align:left"><span class="nowrap"><a href="/wiki/2020_PN1" title="2020 PN1">2020 PN<span style="position: relative; top: 0.3em;"><span style="font-size:80%;">1</span></span></a></span></td> <td>0.127</td> <td>10–50</td> <td><a href="/wiki/Asteroid_Terrestrial-impact_Last_Alert_System" title="Asteroid Terrestrial-impact Last Alert System">ATLAS-HKO</a></td> <td>2020-08-12</td> <td><a class="mw-selflink selflink">Horseshoe orbit</a> temporary</td> <td><a class="mw-selflink selflink">Horseshoe orbit</a> temporary </td></tr> <tr style="background:#E9E9E9"> <td style="text-align:left"><span class="nowrap"><a href="/wiki/2020_PP1" title="2020 PP1">2020 PP<span style="position: relative; top: 0.3em;"><span style="font-size:80%;">1</span></span></a></span></td> <td>0.074</td> <td>10–20</td> <td><a href="/wiki/Pan-STARRS" title="Pan-STARRS">Pan-STARRS</a></td> <td>2020-08-12</td> <td><a href="/wiki/Quasi-satellite" title="Quasi-satellite">Quasi-satellite</a> stable</td> <td><a href="/wiki/Quasi-satellite" title="Quasi-satellite">Quasi-satellite</a> stable </td></tr> <tr style="background:#C2FFFF"> <td style="text-align:left"><span class="nowrap"><a href="/wiki/(614689)_2020_XL5" title="(614689) 2020 XL5">(614689) 2020 XL<span style="position: relative; top: 0.3em;"><span style="font-size:80%;">5</span></span></a></span></td> <td>0.387</td> <td>1100-1260</td> <td><a href="/wiki/Pan-STARRS" title="Pan-STARRS">Pan-STARRS</a></td> <td>2020-12-12</td> <td><a href="/wiki/Earth_trojan" title="Earth trojan">Earth trojan</a></td> <td><a href="/wiki/Earth_trojan" title="Earth trojan">Earth trojan</a> </td></tr> <tr> <td style="text-align:left"><span class="nowrap"><a href="/wiki/2022_NX1" title="2022 NX1">2022 NX<span style="position: relative; top: 0.3em;"><span style="font-size:80%;">1</span></span></a></span></td> <td>0.025</td> <td>5-15</td> <td>Moonbase South Observatory</td> <td>2020-07-02</td> <td>Temporary satellite</td> <td><a href="/wiki/Apollo_asteroid" title="Apollo asteroid">Apollo asteroid</a> </td></tr> <tr style="background:#E9E9E9"> <td style="text-align:left"><span class="nowrap"><a href="/wiki/2023_FW13" title="2023 FW13">2023 FW<span style="position: relative; top: 0.3em;"><span style="font-size:80%;">13</span></span></a></span></td> <td>0.177</td> <td>10-20</td> <td><a href="/wiki/Pan-STARRS" title="Pan-STARRS">Pan-STARRS</a></td> <td>2023-03-28</td> <td><a href="/wiki/Quasi-satellite" title="Quasi-satellite">Quasi-satellite</a></td> <td><a href="/wiki/Quasi-satellite" title="Quasi-satellite">Quasi-satellite</a> </td></tr> <tr> <td style="text-align:left"><span class="nowrap"><a href="/wiki/2024_PT5" title="2024 PT5">2024 PT<span style="position: relative; top: 0.3em;"><span style="font-size:80%;">5</span></span></a></span></td> <td>0.021</td> <td>7–13</td> <td><a href="/wiki/Asteroid_Terrestrial-impact_Last_Alert_System" title="Asteroid Terrestrial-impact Last Alert System">ATLAS South Africa, Sutherland</a></td> <td>2024-08-07</td> <td><a href="/wiki/Temporary_satellite" title="Temporary satellite">Temporary satellite</a></td> <td><a href="/wiki/Temporary_satellite" title="Temporary satellite">Temporary satellite</a> </td></tr></tbody></table> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Horseshoe_orbit&action=edit&section=6" title="Edit section: See also"><span>edit</span></a><span 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id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Horseshoe_orbit&action=edit&section=7" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output 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a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite id="CITEREFChristouAsher2011" class="citation journal cs1">Christou, Apostolos A.; Asher, David J. (2011). <a rel="nofollow" class="external text" href="https://doi.org/10.1111%2Fj.1365-2966.2011.18595.x">"A long-lived horseshoe companion to the Earth"</a>. <i>Monthly Notices of the Royal Astronomical Society</i>. <b>414</b> (4): 2965–2969. <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://arxiv.org/abs/1104.0036">1104.0036</a></span>. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2011MNRAS.414.2965C">2011MNRAS.414.2965C</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1111%2Fj.1365-2966.2011.18595.x">10.1111/j.1365-2966.2011.18595.x</a></span>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:13832179">13832179</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Monthly+Notices+of+the+Royal+Astronomical+Society&rft.atitle=A+long-lived+horseshoe+companion+to+the+Earth&rft.volume=414&rft.issue=4&rft.pages=2965-2969&rft.date=2011&rft_id=info%3Aarxiv%2F1104.0036&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A13832179%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1111%2Fj.1365-2966.2011.18595.x&rft_id=info%3Abibcode%2F2011MNRAS.414.2965C&rft.aulast=Christou&rft.aufirst=Apostolos+A.&rft.au=Asher%2C+David+J.&rft_id=https%3A%2F%2Fdoi.org%2F10.1111%252Fj.1365-2966.2011.18595.x&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHorseshoe+orbit" class="Z3988"></span></span> </li> <li id="cite_note-Fuentes-horseshoe-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-Fuentes-horseshoe_2-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFde_la_Fuente_Marcosde_la_Fuente_Marcos2016" class="citation journal cs1">de la Fuente Marcos, C.; de la Fuente Marcos, R. (April 2016). "A trio of horseshoes: past, present and future dynamical evolution of Earth co-orbital asteroids <span class="nowrap">2015 XX<sub>169</sub></span>, 2015 YA and <span class="nowrap">2015 YQ<sub>1</sub></span>". <i>Astrophysics and Space Science</i>. <b>361</b> (4): 121–133. <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://arxiv.org/abs/1603.02415">1603.02415</a></span>. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2016Ap&SS.361..121D">2016Ap&SS.361..121D</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1007%2Fs10509-016-2711-6">10.1007/s10509-016-2711-6</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:119222384">119222384</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Astrophysics+and+Space+Science&rft.atitle=A+trio+of+horseshoes%3A+past%2C+present+and+future+dynamical+evolution+of+Earth+co-orbital+asteroids+%3Cspan+class%3D%22nowrap%22%3E2015+XX%3Csub%3E169%3C%2Fsub%3E%3C%2Fspan%3E%2C+2015+YA+and+%3Cspan+class%3D%22nowrap%22%3E2015+YQ%3Csub%3E1%3C%2Fsub%3E%3C%2Fspan%3E&rft.volume=361&rft.issue=4&rft.pages=121-133&rft.date=2016-04&rft_id=info%3Aarxiv%2F1603.02415&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A119222384%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1007%2Fs10509-016-2711-6&rft_id=info%3Abibcode%2F2016Ap%26SS.361..121D&rft.aulast=de+la+Fuente+Marcos&rft.aufirst=C.&rft.au=de+la+Fuente+Marcos%2C+R.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHorseshoe+orbit" class="Z3988"></span></span> </li> <li id="cite_note-Fuentes-2016HO3-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-Fuentes-2016HO3_3-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFde_la_Fuente_Marcosde_la_Fuente_Marcos2016" class="citation journal cs1">de la Fuente Marcos, C.; de la Fuente Marcos, R. (November 11, 2016). <a rel="nofollow" class="external text" href="https://doi.org/10.1093%2Fmnras%2Fstw1972">"Asteroid (469219) <span class="nowrap">(469219) 2016 HO<sub>3</sub></span>, the smallest and closest Earth quasi-satellite"</a>. <i>Monthly Notices of the Royal Astronomical Society</i>. <b>462</b> (4): 3441–3456. <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://arxiv.org/abs/1608.01518">1608.01518</a></span>. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2016MNRAS.462.3441D">2016MNRAS.462.3441D</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1093%2Fmnras%2Fstw1972">10.1093/mnras/stw1972</a></span>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:118580771">118580771</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Monthly+Notices+of+the+Royal+Astronomical+Society&rft.atitle=Asteroid+%28469219%29+%3Cspan+class%3D%22nowrap%22%3E%28469219%29+2016+HO%3Csub%3E3%3C%2Fsub%3E%3C%2Fspan%3E%2C+the+smallest+and+closest+Earth+quasi-satellite&rft.volume=462&rft.issue=4&rft.pages=3441-3456&rft.date=2016-11-11&rft_id=info%3Aarxiv%2F1608.01518&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A118580771%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1093%2Fmnras%2Fstw1972&rft_id=info%3Abibcode%2F2016MNRAS.462.3441D&rft.aulast=de+la+Fuente+Marcos&rft.aufirst=C.&rft.au=de+la+Fuente+Marcos%2C+R.&rft_id=https%3A%2F%2Fdoi.org%2F10.1093%252Fmnras%252Fstw1972&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHorseshoe+orbit" class="Z3988"></span></span> </li> <li id="cite_note-MarsHorseshoe-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-MarsHorseshoe_4-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFde_la_Fuente_Marcosde_la_Fuente_Marcos2021" class="citation journal cs1">de la Fuente Marcos, Carlos; de la Fuente Marcos, Raúl (March 2021). <a rel="nofollow" class="external text" href="https://academic.oup.com/mnras/article-abstract/501/4/6007/6081058">"Using Mars co-orbitals to estimate the importance of rotation-induced YORP break-up events in Earth co-orbital space"</a>. <i><a href="/wiki/Monthly_Notices_of_the_Royal_Astronomical_Society" title="Monthly Notices of the Royal Astronomical Society">Monthly Notices of the Royal Astronomical Society</a></i>. <b>501</b> (4): 6007–6025. <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://arxiv.org/abs/2101.02563">2101.02563</a></span>. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2021MNRAS.501.6007D">2021MNRAS.501.6007D</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1093%2Fmnras%2Fstab062">10.1093/mnras/stab062</a></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Monthly+Notices+of+the+Royal+Astronomical+Society&rft.atitle=Using+Mars+co-orbitals+to+estimate+the+importance+of+rotation-induced+YORP+break-up+events+in+Earth+co-orbital+space&rft.volume=501&rft.issue=4&rft.pages=6007-6025&rft.date=2021-03&rft_id=info%3Aarxiv%2F2101.02563&rft_id=info%3Adoi%2F10.1093%2Fmnras%2Fstab062&rft_id=info%3Abibcode%2F2021MNRAS.501.6007D&rft.aulast=de+la+Fuente+Marcos&rft.aufirst=Carlos&rft.au=de+la+Fuente+Marcos%2C+Ra%C3%BAl&rft_id=https%3A%2F%2Facademic.oup.com%2Fmnras%2Farticle-abstract%2F501%2F4%2F6007%2F6081058&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHorseshoe+orbit" class="Z3988"></span></span> </li> </ol></div></div> <div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Horseshoe_orbit&action=edit&section=8" title="Edit section: External links"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a rel="nofollow" class="external text" href="http://www.scielo.br/pdf/cam/v24n1/06v24n1.pdf">Research paper describing Horseshoe orbits.</a> Start at page 105.</li> <li><a rel="nofollow" class="external text" href="http://www.astro.uwo.ca/~wiegert/AA29/AA29.html">A good description of <i>2002 AA29</i></a></li></ul> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><style data-mw-deduplicate="TemplateStyles:r1236075235">.mw-parser-output .navbox{box-sizing:border-box;border:1px solid #a2a9b1;width:100%;clear:both;font-size:88%;text-align:center;padding:1px;margin:1em auto 0}.mw-parser-output .navbox .navbox{margin-top:0}.mw-parser-output .navbox+.navbox,.mw-parser-output .navbox+.navbox-styles+.navbox{margin-top:-1px}.mw-parser-output .navbox-inner,.mw-parser-output .navbox-subgroup{width:100%}.mw-parser-output .navbox-group,.mw-parser-output .navbox-title,.mw-parser-output .navbox-abovebelow{padding:0.25em 1em;line-height:1.5em;text-align:center}.mw-parser-output .navbox-group{white-space:nowrap;text-align:right}.mw-parser-output .navbox,.mw-parser-output .navbox-subgroup{background-color:#fdfdfd}.mw-parser-output .navbox-list{line-height:1.5em;border-color:#fdfdfd}.mw-parser-output .navbox-list-with-group{text-align:left;border-left-width:2px;border-left-style:solid}.mw-parser-output tr+tr>.navbox-abovebelow,.mw-parser-output tr+tr>.navbox-group,.mw-parser-output tr+tr>.navbox-image,.mw-parser-output tr+tr>.navbox-list{border-top:2px solid #fdfdfd}.mw-parser-output .navbox-title{background-color:#ccf}.mw-parser-output .navbox-abovebelow,.mw-parser-output .navbox-group,.mw-parser-output .navbox-subgroup .navbox-title{background-color:#ddf}.mw-parser-output .navbox-subgroup .navbox-group,.mw-parser-output .navbox-subgroup .navbox-abovebelow{background-color:#e6e6ff}.mw-parser-output .navbox-even{background-color:#f7f7f7}.mw-parser-output .navbox-odd{background-color:transparent}.mw-parser-output .navbox .hlist td dl,.mw-parser-output .navbox .hlist td ol,.mw-parser-output .navbox .hlist td ul,.mw-parser-output .navbox td.hlist dl,.mw-parser-output .navbox td.hlist ol,.mw-parser-output .navbox td.hlist ul{padding:0.125em 0}.mw-parser-output .navbox .navbar{display:block;font-size:100%}.mw-parser-output .navbox-title .navbar{float:left;text-align:left;margin-right:0.5em}body.skin--responsive .mw-parser-output .navbox-image img{max-width:none!important}@media print{body.ns-0 .mw-parser-output .navbox{display:none!important}}</style></div><div role="navigation" class="navbox" aria-labelledby="Gravitational_orbits" style="padding:3px"><table class="nowraplinks hlist mw-collapsible expanded navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239400231"><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Orbits" title="Template:Orbits"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Orbits" title="Template talk:Orbits"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Orbits" title="Special:EditPage/Template:Orbits"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Gravitational_orbits" style="font-size:114%;margin:0 4em">Gravitational <a href="/wiki/Orbit" title="Orbit">orbits</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/List_of_orbits" title="List of orbits">Types</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:6em">General</th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Box_orbit" title="Box orbit">Box</a></li> <li><a href="/wiki/Parabolic_trajectory" title="Parabolic trajectory">Capture</a></li> <li><a href="/wiki/Circular_orbit" title="Circular orbit">Circular</a></li> <li><a href="/wiki/Elliptic_orbit" title="Elliptic orbit">Elliptical</a> / <a href="/wiki/Highly_elliptical_orbit" title="Highly elliptical orbit">Highly elliptical</a></li> <li><a href="/wiki/Parabolic_trajectory" title="Parabolic trajectory">Escape</a></li> <li><a class="mw-selflink selflink">Horseshoe</a></li> <li><a href="/wiki/Hyperbolic_trajectory" title="Hyperbolic trajectory">Hyperbolic trajectory</a></li> <li><a href="/wiki/Inclined_orbit" title="Inclined orbit">Inclined</a> / <a href="/wiki/Non-inclined_orbit" class="mw-redirect" title="Non-inclined orbit">Non-inclined</a></li> <li><a href="/wiki/Kepler_orbit" title="Kepler orbit">Kepler</a></li> <li><a href="/wiki/Lagrange_point" title="Lagrange point">Lagrange point</a></li> <li><a href="/wiki/Osculating_orbit" title="Osculating orbit">Osculating</a></li> <li><a href="/wiki/Parabolic_trajectory" title="Parabolic trajectory">Parabolic trajectory</a></li> <li><a href="/wiki/Parking_orbit" title="Parking orbit">Parking</a></li> <li><a href="/wiki/Retrograde_and_prograde_motion" title="Retrograde and prograde motion">Prograde / Retrograde</a></li> <li><a href="/wiki/Synchronous_orbit" title="Synchronous orbit">Synchronous</a> <ul><li><a href="/wiki/Semi-synchronous_orbit" title="Semi-synchronous orbit">semi</a></li> <li><a href="/wiki/Subsynchronous_orbit" title="Subsynchronous orbit">sub</a></li></ul></li> <li><a href="/wiki/Hohmann_transfer_orbit" title="Hohmann transfer orbit">Transfer orbit</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:6em"><a href="/wiki/Geocentric_orbit" title="Geocentric orbit">Geocentric</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Geosynchronous_orbit" title="Geosynchronous orbit">Geosynchronous</a> <ul><li><a href="/wiki/Geostationary_orbit" title="Geostationary orbit">Geostationary</a></li> <li><a href="/wiki/Geostationary_transfer_orbit" title="Geostationary transfer orbit">Geostationary transfer</a></li></ul></li> <li><a href="/wiki/Graveyard_orbit" title="Graveyard orbit">Graveyard</a></li> <li><a href="/wiki/High_Earth_orbit" title="High Earth orbit">High Earth</a></li> <li><a href="/wiki/Low_Earth_orbit" title="Low Earth orbit">Low Earth</a></li> <li><a href="/wiki/Medium_Earth_orbit" title="Medium Earth orbit">Medium Earth</a></li> <li><a href="/wiki/Molniya_orbit" title="Molniya orbit">Molniya</a></li> <li><a href="/wiki/Near-equatorial_orbit" title="Near-equatorial orbit">Near-equatorial</a></li> <li><a href="/wiki/Orbit_of_the_Moon" title="Orbit of the Moon">Orbit of the Moon</a></li> <li><a href="/wiki/Polar_orbit" title="Polar orbit">Polar</a></li> <li><a href="/wiki/Sun-synchronous_orbit" title="Sun-synchronous orbit">Sun-synchronous</a></li> <li><a href="/wiki/Transatmospheric_orbit" title="Transatmospheric orbit">Transatmospheric</a></li> <li><a href="/wiki/Tundra_orbit" title="Tundra orbit">Tundra</a></li> <li><a href="/wiki/Very_low_Earth_orbit" title="Very low Earth orbit">Very low Earth</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:6em">About<br />other points</th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em"> <ul><li>Mars <ul><li><a href="/wiki/Areocentric_orbit" title="Areocentric orbit">Areocentric</a></li> <li><a href="/wiki/Areosynchronous_orbit" title="Areosynchronous orbit">Areosynchronous</a></li> <li><a href="/wiki/Areostationary_orbit" title="Areostationary orbit">Areostationary</a></li></ul></li> <li>Lagrange points <ul><li><a href="/wiki/Distant_retrograde_orbit" title="Distant retrograde orbit">Distant retrograde</a></li> <li><a href="/wiki/Halo_orbit" title="Halo orbit">Halo</a></li> <li><a href="/wiki/Lissajous_orbit" title="Lissajous orbit">Lissajous</a></li> <li><a href="/wiki/Libration_point_orbit" title="Libration point orbit">Libration</a></li></ul></li> <li><a href="/wiki/Lunar_orbit" title="Lunar orbit">Lunar</a></li> <li>Sun <ul><li><a href="/wiki/Heliocentric_orbit" title="Heliocentric orbit">Heliocentric</a> <ul><li><a href="/wiki/Earth%27s_orbit" title="Earth's orbit">Earth's orbit</a></li></ul></li> <li><a href="/wiki/Mars_cycler" title="Mars cycler">Mars cycler</a></li> <li><a href="/wiki/Sun-synchronous_orbit" title="Sun-synchronous orbit">Heliosynchronous</a></li></ul></li> <li>Other <ul><li><a href="/wiki/Lunar_cycler" title="Lunar cycler">Lunar cycler</a></li></ul></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Orbital_elements" title="Orbital elements">Parameters</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:6em"><div class="hlist"><ul><li>Shape</li><li>Size</li></ul></div></th><td class="navbox-list-with-group navbox-list navbox-even" style="padding:0"><div style="padding:0 0.25em"> <ul><li><span class="texhtml mvar" style="font-style:italic;">e</span>  <a href="/wiki/Orbital_eccentricity" title="Orbital eccentricity">Eccentricity</a></li> <li><span class="texhtml mvar" style="font-style:italic;">a</span>  <a href="/wiki/Semi-major_and_semi-minor_axes" title="Semi-major and semi-minor axes">Semi-major axis</a></li> <li><span class="texhtml mvar" style="font-style:italic;">b</span>  <a href="/wiki/Semi-major_and_semi-minor_axes" title="Semi-major and semi-minor axes">Semi-minor axis</a></li> <li><span class="texhtml mvar" style="font-style:italic;">Q</span>, <span class="texhtml mvar" style="font-style:italic;">q</span>  <a href="/wiki/Apsis" title="Apsis">Apsides</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:6em">Orientation</th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em"> <ul><li><span class="texhtml mvar" style="font-style:italic;">i</span>  <a href="/wiki/Orbital_inclination" title="Orbital inclination">Inclination</a></li> <li><span class="texhtml mvar" style="font-style:italic;">Ω</span>  <a href="/wiki/Longitude_of_the_ascending_node" title="Longitude of the ascending node">Longitude of the ascending node</a></li> <li><span class="texhtml mvar" style="font-style:italic;">ω</span>  <a href="/wiki/Argument_of_periapsis" title="Argument of periapsis">Argument of periapsis</a></li> <li><span class="texhtml mvar" style="font-style:italic;">ϖ</span>  <a href="/wiki/Longitude_of_the_periapsis" class="mw-redirect" title="Longitude of the periapsis">Longitude of the periapsis</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:6em">Position</th><td class="navbox-list-with-group navbox-list navbox-even" style="padding:0"><div style="padding:0 0.25em"> <ul><li><span class="texhtml mvar" style="font-style:italic;">M</span>  <a href="/wiki/Mean_anomaly" title="Mean anomaly">Mean anomaly</a></li> <li><span class="texhtml mvar" style="font-style:italic;">ν</span>, <span class="texhtml mvar" style="font-style:italic;">θ</span>, <span class="texhtml mvar" style="font-style:italic;">f</span>  <a href="/wiki/True_anomaly" title="True anomaly">True anomaly</a></li> <li><span class="texhtml mvar" style="font-style:italic;">E</span>  <a href="/wiki/Eccentric_anomaly" title="Eccentric anomaly">Eccentric anomaly</a></li> <li><span class="texhtml mvar" style="font-style:italic;">L</span>  <a href="/wiki/Mean_longitude" title="Mean longitude">Mean longitude</a></li> <li><span class="texhtml mvar" style="font-style:italic;">l</span>  <a href="/wiki/True_longitude" title="True longitude">True longitude</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:6em">Variation</th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em"> <ul><li><span class="texhtml mvar" style="font-style:italic;">T</span>  <a href="/wiki/Orbital_period" title="Orbital period">Orbital period</a></li> <li><span class="texhtml mvar" style="font-style:italic;">n</span>  <a href="/wiki/Mean_motion" title="Mean motion">Mean motion</a></li> <li><span class="texhtml mvar" style="font-style:italic;">v</span>  <a href="/wiki/Orbital_speed" title="Orbital speed">Orbital speed</a></li> <li><span class="texhtml"><i>t</i><sub>0</sub></span>  <a href="/wiki/Epoch_(astronomy)" title="Epoch (astronomy)">Epoch</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Orbital_maneuver" title="Orbital maneuver">Maneuvers</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Bi-elliptic_transfer" title="Bi-elliptic transfer">Bi-elliptic transfer</a></li> <li><a href="/wiki/Collision_avoidance_(spacecraft)" title="Collision avoidance (spacecraft)">Collision avoidance (spacecraft)</a></li> <li><a href="/wiki/Delta-v" title="Delta-v">Delta-v</a></li> <li><a href="/wiki/Delta-v_budget" title="Delta-v budget">Delta-v budget</a></li> <li><a href="/wiki/Gravity_assist" title="Gravity assist">Gravity assist</a></li> <li><a href="/wiki/Gravity_turn" title="Gravity turn">Gravity turn</a></li> <li><a href="/wiki/Hohmann_transfer_orbit" title="Hohmann transfer orbit">Hohmann transfer</a></li> <li><a href="/wiki/Orbital_inclination_change" title="Orbital inclination change">Inclination change</a></li> <li><a href="/wiki/Low-energy_transfer" title="Low-energy transfer">Low-energy transfer</a></li> <li><a href="/wiki/Oberth_effect" title="Oberth effect">Oberth effect</a></li> <li><a href="/wiki/Orbit_phasing" title="Orbit phasing">Phasing</a></li> <li><a href="/wiki/Tsiolkovsky_rocket_equation" title="Tsiolkovsky rocket equation">Rocket equation</a></li> <li><a href="/wiki/Space_rendezvous" title="Space rendezvous">Rendezvous</a></li> <li><a href="/wiki/Trans-lunar_injection" title="Trans-lunar injection">Trans-lunar injection</a></li> <li><a href="/wiki/Transposition,_docking,_and_extraction" title="Transposition, docking, and extraction">Transposition, docking, and extraction</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Orbital_mechanics" title="Orbital mechanics">Orbital<br />mechanics</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Astronomical_coordinate_systems" title="Astronomical coordinate systems">Astronomical coordinate systems</a></li> <li><a href="/wiki/Characteristic_energy" title="Characteristic energy">Characteristic energy</a></li> <li><a href="/wiki/Escape_velocity" title="Escape velocity">Escape velocity</a></li> <li><a href="/wiki/Ephemeris" title="Ephemeris">Ephemeris</a></li> <li><a href="/wiki/Equatorial_coordinate_system" title="Equatorial coordinate system">Equatorial coordinate system</a></li> <li><a href="/wiki/Ground_track" class="mw-redirect" title="Ground track">Ground track</a></li> <li><a href="/wiki/Hill_sphere" title="Hill sphere">Hill sphere</a></li> <li><a href="/wiki/Interplanetary_Transport_Network" title="Interplanetary Transport Network">Interplanetary Transport Network</a></li> <li><a href="/wiki/Kepler%27s_laws_of_planetary_motion" title="Kepler's laws of planetary motion">Kepler's laws of planetary motion</a></li> <li><a href="/wiki/Lagrange_point" title="Lagrange point">Lagrangian point</a></li> <li><a href="/wiki/N-body_problem" title="N-body problem"><i>n</i>-body problem</a></li> <li><a href="/wiki/Orbit_equation" title="Orbit equation">Orbit equation</a></li> <li><a href="/wiki/Orbital_state_vectors" title="Orbital state vectors">Orbital state vectors</a></li> <li><a href="/wiki/Perturbation_(astronomy)" title="Perturbation (astronomy)">Perturbation</a></li> <li><a href="/wiki/Retrograde_and_prograde_motion" title="Retrograde and prograde motion">Retrograde and prograde motion</a></li> <li><a href="/wiki/Specific_orbital_energy" title="Specific orbital energy">Specific orbital energy</a></li> <li><a href="/wiki/Specific_angular_momentum" title="Specific angular momentum">Specific angular momentum</a></li> <li><a href="/wiki/Two-line_element_set" title="Two-line element set">Two-line elements</a></li></ul> </div></td></tr><tr><td class="navbox-abovebelow" colspan="2"><div> <ul><li><span class="noviewer" typeof="mw:File"><span title="List-Class article"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/d/db/Symbol_list_class.svg/16px-Symbol_list_class.svg.png" decoding="async" width="16" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/d/db/Symbol_list_class.svg/23px-Symbol_list_class.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/d/db/Symbol_list_class.svg/31px-Symbol_list_class.svg.png 2x" data-file-width="180" data-file-height="185" /></span></span> <a href="/wiki/List_of_orbits" title="List of orbits">List of orbits</a></li></ul> </div></td></tr></tbody></table></div>    </div><noscript><img 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